Middle School Math

Open Window seeks to balance a commitment to allowing each child to work to his/her potential in mathematics with a structure that provides for an adequate amount of direct instruction, student collaboration, and teacher-student interaction. We offer a sequence of six math courses in middle school: Math Foundations 1, Math Foundations 2, Pre-Algebra, High School Algebra 1, High School Geometry and High School Algebra 2.  Although many supplemental materials are used, the Prentice-Hall mathematics series serves as the core text and is designed to help students develop a deeper understanding of math through an emphasis on thinking, reasoning, and problem-solving.
 
In designing a middle school math sequence for gifted students, Open Window offers opportunity for both acceleration and enrichment through a focus on problem-solving and application.  All middle school students will complete one year of high school level math (Algebra 1), many Geometry, and a few Algebra 2.
 
Students taking high school level classes are not guaranteed to earn high school credit (this is determined by receiving high schools); however, students who perform satisfactorily at Open Window should receive placement into the next level in high school.  Open Window administers a standardized End of Course exam which serves as a tangible indication of successfully completing a high school level course.

Math Foundations 1

This class covers material typically covered in sixth grade mathematics textbooks. Foundations 1 covers a combination of rational numbers, patterns, geometry, and integers in preparation for one-step and two-step equations and inequalities.  Instruction introduces division with decimals. By the end of the year, each student must demonstrate mastery of all four operations with decimals. After reviewing basic fraction concepts, fractions are used to add, subtract, multiply and divide with an emphasis on understanding divisibility rules and factoring. Problem solving with percentages is introduced. Higher level thinking is pursued, introducing strategies for solving multi-step problems and working backwards. Throughout the year an emphasis is placed on recognizing patterns, and describing them mathematically. 
 
Course Materials 
  • Prentice Hall Mathematics Course 1
  • Teacher created materials
  • Activities and Projects developed by Math For Love
  • Student Notebook Portfolio

Pre-Algebra

Pre-Algebra provides a solid mathematical foundation in order to fully prepare students for the study of high-school level Algebra.During the study of Pre-Algebra, students will develop their mathematical reasoning, algebraic thinking skills, and computational accuracy for future work in mathematics. To this end, some major goals for students in Pre-Algebra are to develop the idea of a variable and evaluate and simplify algebraic expressions, skillfully perform operations on integers and then all rational numbers, solve equations, understand and use the exponent rules, perform operations on polynomials, graph linear equations and inequalities on a coordinate plane by the slope-intercept method, discuss basic probability and statistics concepts, expand the ideas of percent, ratio and proportion, discuss and write about mathematical ideas, solve problems requiring different strategies and relate math to today’s life and careers.
 
Course Materials 
  • Prentice Hall Mathematics Course 3                                 
  • The Art of Problem Solving: Pre-Algebra
  • Additional teacher resources for projects and enrichment activities
  • Activities and Projects developed by Math For Love
  • Student Notebook Portfolio

Geometry

Geometry at Open Window is offered to students who have successfully completed a year of high-school level Algebra. This course covers tools of geometry, inductive and deductive reasoning and proofs in Algebra and Geometry. Topics also include: parallel and perpendicular lines, proving triangles congruent, using congruent triangles, isosceles and equilateral triangles, congruence in right triangles, relationships within triangles, concurrent lines and inequalities in triangles, quadrilaterals and their properties, coordinate geometry proofs, proportions and similarity, trigonometric ratios and angles of elevation and depression, the Pythagorean Theorem and special right triangles, different types of transformations, areas of regular polygons, circles, sectors and geometric probability, surface area and volume of 3D figures, tangent lines, chords and arcs, inscribed angles, angle measures and segment length, circles in coordinate plane and locus. Algebra is integrated where appropriate, such as simplifying radicals and solving using quadratic equations and systems of linear equations.
 
Course Materials  
  • Prentice Hall Geometry
  • The Art of Problem Solving: Introduction to Geometry
  • Additional teacher resources for projects and enrichment activities
  • Student Notebook Portfolio

Math Foundations 2

Foundations 2 features a structured approach to ratios, percentages, equations, inequalities, geometry, graphing and probability.  Instruction initially reviews the use of decimals and fractions, focusing on mixed numbers. By the end of the year, students should demonstrate mastery of all four operations with fractions.  Students will progress to computations with integers without depending upon the use of manipulatives. Formulas are used in the study of geometric shapes. Solving problems with percentages is accomplished using algebraic equations. A unit on probability and statistics will be included in this class along with enrichment activities that broaden the students’ mathematical foundation.
 
Course Materials
  • Prentice Hall Mathematics, Course 2
  • Additional teacher resources for projects and enrichment activities
  • Activities and Projects developed by Math For Love
  • Student Notebook Portfolio

Algebra 1

A comprehensive course in high school-level Algebra is completed by all Open Window students. Areas of study include: variables, function patterns and graphs, rational numbers, solving equations and inequalities, different forms of linear equations and their graphs, systems of equations and inequalities, exponents and exponential functions, polynomials and factoring, quadratic equations and functions, radical expressions and equations, simplifying rational expressions. 
 
Course Materials
  • Prentice Hall Algebra I
  • The Art of Problem Solving: Introduction to Algebra
  • Additional teacher resources for projects and enrichment activities
  • Student Notebook Portfolio
 
 
 

Algebra 2

Algebra 2 at Open Window is offered to students who have successfully completed a year of high-school level Algebra and Geometry. Required areas of study include: functions and relations, linear and absolute value functions, systems of linear equations and inequalities, matrices, quadratic functions and complex numbers, polynomials and polynomial functions, exponential and logarithmic functions, rational and radical expressions and functions, quadratic relations and conic sections, sequences and series, probability and data analysis. Trigonometry is covered if time permits. 
 
Course Materials 
  • Prentice Hall Algebra II
  • Art of Problem Solving Intermediate Algebra
  • Additional teacher resources for projects and enrichment activities
  • Student Notebook Portfolio